TOPOLOGICAL CHARACTERIZATION FOR
THE LINE GRAPH OF NANOSTRUCTURES
Jianzhong Xu1, Muhammad K. Siddiqui2,
Muhammad Imran3,4
1 Department of Electronics and Information Engineering
Bozhou University, Bozhou 236800, CHINA
2 Department of Mathematics
COMSATS University Islamabad
Lahore Campus, 54000 - PAKISTAN
3 Department of Mathematical Sciences
United Arab Emirates University, P.O. Box 15551
Al Ain, UNITED ARAB EMIRATES
4 Department of Mathematics
School of Natural Sciences (SNS)
National University of Sciences and Technology (NUST)
Sector H-12, Islamabad, PAKISTAN

Abstract

A numerical quantity that characterizes the whole structure of a graph is called a topological index. More preciously topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity/ property/ toxicity relationships. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. The concepts of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials were established in chemical graph theory based on vertex degrees. These indices are useful in the study of anti-inflammatory activities of certain chemical networks. In this paper, we determine the hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials of the line graph of $2D-$lattice, nanotube and nanotorus of $TUC_4C_8[p,q]$ by using the concept of subdivision.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 6
Year: 2019

DOI: 10.12732/ijam.v32i6.11

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